The objective of the air-charge control in lean-burn, spark-ignited engines is to operate the electronic throttle and the EGR valve in a manner so as to provide the desired gas flow to the engine and the desired burnt gas fraction in this flow for NO.sub.x reduction. The conventional approach to the air-charge control is open-loop whereby the desired mass flow rates through the EGR valve and throttle are calculated as functions of the desired burnt gas fraction in the intake manifold and of the desired gas flow into the cylinder. The desired values of the EGR valve position and of the throttle position are backtracked using an orifice equation with known effective flow area map. Suppose F.sub.1,d is the desired burn gas fraction, W.sub.cyl,d is the desired gas flow rate into the cylinder. The desired mass flow rate through the throttle and the desired mass flow rate through the EGR valve can be calculated as follows: EQU W.sub.th,d =(W.sub.cyl,d -W.sub.egr,d), EQU W.sub.egr,d =(F.sub.1,d (W.sub.cyl,d +W.sub.f)W.sub.cyl,d /W.sub.f /(1+.lambda..sub.s)),
where .lambda..sub.s is the stoichiometric air-to-fuel ratio and W.sub.f is the engine fueling rate. The desired throttle position, u.sub.th, is determined from the intake manifold pressure p.sub.1, ambient pressure, p.sub.amb, and ambient temperature, T.sub.amb, while the estimate of exhaust manifold temperature T.sub.2 and exhaust manifold pressure p.sub.2 as well as a measurement of p.sub.1 are used to calculate the EGR valve position u.sub.egr. Typically, the values of F.sub.1,d, W.sub.cyl,d are functions of engine speed, engine torque, combustion mode, etc., determined by calibration tables that are optimized for fuel economy and emissions.
There are several problems with the conventional approach. First, the soot deposits in the EGR valve and pipes change the effective flow area of the valve. This problem is particularly severe with lean-burn, direct-injection, spark-ignition engines. Second, depending on the EGR valve and throttle type, calibration drifts may render their actual position uncertain. Due to these uncertainties, the desired mass flow rates may not be achieved with the open-loop approach; and the emission performance of the engine at a given engine speed and engine load point may be shifted away from the desired nominal performance. Even without the calibration drift, when the pressure drop across the throttle or the EGR valve is small, the open-loop procedure may lead to excessive chattering of the desired throttle position or EGR valve position due to noise in the pressure measurements. Other sources of uncertainty, such as changes in the engine back pressure due to the exhaust tract clogging, may also affect the engine operation in substantial ways.
More specifically, consider FIGS. 1-3. The dashed lines in these figures correspond to the steady-state values of the NO.sub.x mass flow rate, engine exhaust temperature and engine torque achieved by the conventional open-loop controller as a function of the unknown multiplier, .theta..sub.egr, on EGR valve effective flow areas. The value of .theta..sub.egr =1 correspond to the nominal case. Constant values of engine speed N=2000 rpm, fueling rate W.sub.f =2 kg/hr, spark timing .delta.=25 deg BTDC and constant desired values of the in-cylinder flow W.sub.cyl,d =80 kg/hr and burnt gas fraction F.sub.1,d =0.1 were used in the engine model simulation. With 40 percent of EGR valve flow area reduction, there is a significant increase in NO.sub.x emissions by 50 percent (see FIG. 1). FIGS. 2 and 3 demonstrate that the engine exhaust temperature and the engine brake torque are affected by changes in .theta..sub.egr. The variations in .theta..sub.egr translate into variations in the burnt gas fraction delivered to the engine and, therefore, engine combustion variations.